Quantum parameter estimation is the theory for quantum metrology, and quantum
Cramér-Rao bound is the most well-studied mathematical tool for quantum
parameter estimation [1]}, [2]}. In quantum Cramér-Rao bound,
the quantum Fisher information (QFI) and quantum Fisher information matrix
(QFIM) are the key quantities representing the precision limit for single
parameter and multiparameter estimations. In recent years, several outstanding
reviews on quantum metrology and quantum parameter estimation have been provided from
different perspectives and at different time, including the ones given by Giovannetti et al.
on the quantum-enhanced measurement [3]} and the advances
in quantum metrology [4]}, the ones given by Paris [5]}
and Toth et al. [6]} on the QFI and its applications in quantum metrology,
the one by Braun et al. on the quantum enhanced metrology without entanglement [7]},
the ones by Pezzè et al. [8]} and Huang et al. [9]} on
quantum metrology with cold atoms, the one by Degen et al. on general quantum sensing [10]},
the one by Pirandola et al. on the photonic quantum sensing [11]},
the ones by Dowling on quantum optical metrology with high-N00N state [12]}
and Dowling and Seshadreesan on theoretical and experimental optical technologies
in quantum metrology, sensing and imaging [13]},
the one by Demkowicz-Dobrzański et al. on the quantum limits in optical
interferometry [14]}, the one by Sidhu and Kok on quantum parameter
estimation from a geometric perspective , and the one by Szczykulska
et al. on simultaneous multiparameter estimation .
Petz et al. also wrote a thorough technical introduction on QFI .
